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In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…
Trade prices of about 1000 New York Stock Exchange-listed stocks are studied at one-minute time resolution over the continuous five year period 2018--2022. For each stock, in dollar-volume-weighted transaction time, the discrepancy from a…
Higher order correlation measurements involve multiple event averages which must run over unequal events to avoid statistical bias. We derive correction formulas for small event samples, where the bias is largest, and utilize the results to…
Stock prices are highly volatile and sudden changes in trends are often very problematic for traditional forecasting models to handle. The standard Long Short Term Memory (LSTM) networks are regarded as the state-of-the-art models for such…
In the current stock market, computer science and technology are more and more widely used to analyse stocks. Not same as most related machine learning stock price prediction work, this work study the predicting the tendency of the stock…
We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
A very common task in data visualization is to plot many data points with some measured y-value as a function of fixed x-values. Uncertainties on the y-values are typically presented as vertical error bars that represent either a…
We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the…
We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
In this paper, we describe two approaches to model the behavior of stock prices. The first approach considers the underlying probability distribution of day-to-day price differences. The second approach models the movement of the price as a…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around…
This study explores the behavioral dynamics of illiquid stock prices in a listed stock market. Illiquidity, characterized by wide bid and ask spreads affects price formation by decoupling prices from standard risk and return relationships…
We investigate the predictability of several range-based stock volatility estimators, and compare them to the standard close-to-close estimator which is most commonly acknowledged as the volatility. The patterns of volatility changes are…
Using frequency distributions of daily closing price time series of several financial market indexes, we investigate whether the bias away from an equiprobable sequence distribution found in the data, predicted by algorithmic information…
We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The…
The best linear unbiased estimator (BLUE) is a popular statistical method adopted to combine multiple measurements of the same observable taking into account individual uncertainties and their correlation. The method is unbiased by…
This paper presents closed-form analytical formulas for pricing volatility and variance derivatives with nonlinear payoffs under discrete-time observations. The analysis is based on a probabilistic approach assuming that the underlying…